[Miron]

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Opps are rather weak, but it shouldn't much matter for my question.
You play infrequently with your partner, so no clear meaning for 2♥.

1♦ - 1♥ - 2♥ - x
?

I choose 2♠ as preparing for doubling 3 or more ♥ (when I have not passed or bid 2NT I cannot have penalty double). Also the bid is descriptive (but partner probably doesn't have 4 spades).

1♦ - 1♥ - 2♥ - x
2♠ - 3♥ - 4♣ - 4♥
x - pass - 4NT - pass
5♠ - pass - 6♦ - pass
?

x: IMHO: The mild slam invitation (as I cannot have the penalty double)
5♠: is some answer doesn't really matter which (you have exactly the same info about 4NT as I had).

What is 6♦? Is it to play or is it Doroszewicz?

[Codo]

2 Heart often is a kind of a strong raise, so 6 ♦ is to play. But I doubt, that your pd had the same thoughts about the bids then you have.

[SoTired]

My guesses:
2H is LR+ for diam. Don't see any use for 2H bid with a strong club suit when 2C would work just fine. That makes 2S & 4C q-bids. And the X is a heart q-bid. 4N is RKC for diam. 5S is 2+DQ. If you assume responder has 5♦ giving you a 10-card fit, you can show the queen, so that is right also.

So I understand and agree with all bids so far.

Opener has 2 choices here - Pass and 7D. I would bid 7D because:

Responder could have bid 4N over 2S, but waited until 4HX showing a heart stopper. So responder seems to have 2 controls outside hearts. Responder has pushed to slam with little encouragement so must have a good hand. You have undisclosed strength with the ♠Q and ♣K. Finally, the opps are bidding wildly in hearts implying that responder has little wasted strength there. Probably 2 or 3 small hearts. I can count 7♦ tricks + 5 black even if partner has only 1 of ♠K/♣Q and needs either an extra diam, a squeeze or at worse a finesse for the 13th trick.